Shaped gradient lens

ABSTRACT

One embodiment provides a method for receiving parallel rays at a lens. A first surface of the lens can receive first substantially parallel rays incoming from a first direction. The first surface of the lens also can receive second substantially parallel rays incoming from a second direction that is substantially different than the first direction. The lens can focus the first substantially parallel rays onto a first focal point on a second surface of the lens and focus the second substantially parallel rays onto a second focal point on the second surface of the lens, the second focal point being different than the first focal point.

RELATED PATENT APPLICATIONS

This patent application claims priority under 35 U.S.C. §119 to U.S.Provisional Patent Application No. 61/150,651, entitled “Shaped GradientLens,” filed Feb. 6, 2009, and is related to U.S. patent applicationSer. No. 12/322,592, entitled “Modal Beam Positioning,” filed on Feb. 4,2009. The entire contents of each of the foregoing priority and relatedapplications are hereby fully incorporated herein by reference.

TECHNICAL FIELD

The invention relates generally to lenses for use in antennacommunications and more particularly to shaped gradient lenses forfocusing parallel rays of electromagnetic energy received at one surfaceof a lens to a focal point on a second surface of the lens for receiptby an antenna feed element.

BACKGROUND

Lenses alter the direction of travel of transmitted electromagneticwaves. Lenses are often used to focus or defocus beams or parallel raysof electromagnetic energy incident on a surface of the lens. Someeveryday devices that use lenses include corrective eyeglasses, cameras,and binoculars. In these applications, the lenses focus electromagneticenergy radiating at optical frequencies. Lenses are also commonly usedfor high frequency electromagnetic radiation, such as microwavefrequencies and frequencies extending into the gigahertz range.

One type of lens is a gradient lens. Typically, a gradient lens is adevice for which the dielectric constant of the material from which thelens is constructed, and thus the index of refraction, varies along apath of a ray representing energy direction of propagation passesthrough the lens. As the ray passes from a first medium having a firstindex of refraction into a second medium having a different index ofrefraction at a direction that is not perpendicular to the boundarybetween the two mediums, the direction of the ray is changed. If thefirst medium has a smaller index of refraction than that of the secondmedium, the ray bends toward a normal perpendicular to the boundary asthe ray passes into the second medium. That is, the ray in the secondmedium is propagating in a direction closer to the normal.

Most lenses focus incoming light to a focal point that is substantiallyremoved from the lens. However, in many applications, it would be usefulfor the focal point(s) of a lens to be on a surface of the lens. Lenseswith focal points on the surface of the lens include Luneburg lenses,Maxwell fisheye lenses and constant-K lenses. These lenses tend to bespheres which can be large and heavy as aperture size increases.Accordingly, a need in the art exists for a lens that can focus parallelrays of electromagnetic energy received at one surface of a lens onto afocal point at a second surface of the lens where the lens is smallerthan a full sphere.

SUMMARY

The present invention provides a gradient lens capable of focusingelectromagnetic rays received at a first lens surface onto a second lenssurface. The first lens surface and second lens surface can includeconvex surfaces protruding in opposite directions from a substantiallyplanar surface. The lens can include a gradient index between the firstsurface and the planar surface and a gradient index between the twoconvex surfaces. The lens can include two or more gradient layers, eachgradient layer having an index of refraction different than that ofadjacent gradient layers. The gradient layers can focus parallel rays ofenergy incident on the first surface onto a focal point at the secondsurface of the lens. As the parallel rays pass from one gradient layerto the next, the rays are redirected toward the focal point.

One aspect of the present invention provides a gradient lens. Thisgradient lens can include a substantially planar surface, a first convexsurface opposite from and projecting outward from the substantiallyplanar surface, a second convex surface opposite from and projectingaway from the first convex surface and forming a protrusion with respectto the substantially planar surface, and a gradient index between thefirst convex surface and the substantially planar surface.

Another aspect of the present invention provides a gradient lens. Thisgradient lens can include a first substantially hemispherical membercomprising a first convex surface and a base. The gradient lens also caninclude a second substantially hemispherical member projecting away fromthe base of the first hemispherical member and comprising a secondconvex surface. Gradient layers can be disposed within the firsthemispherical member. Each gradient layer can be concentrically alignedto the first hemispherical member and include an index of refractiondifferent than that of adjacent gradient layers.

Another aspect of the present invention provides a method for receivingparallel rays at a lens. A first surface of the lens can receive firstsubstantially parallel rays incoming from a first direction. The firstsurface of the lens also can receive second substantially parallel raysincoming from a second direction that is substantially different thanthe first direction. The lens can focus the first substantially parallelrays onto a first focal point on a second surface of the lens and focusthe second substantially parallel rays onto a second focal point on thesecond surface of the lens, the second focal point being different thanthe first focal point.

The discussion of gradient lenses presented in this summary is forillustrative purposes only. Various aspects of the present invention maybe more clearly understood and appreciated from a review of thefollowing detailed description of the disclosed embodiments and byreference to the drawings and the claims that follow. Moreover, otheraspects, systems, methods, features, advantages, and objects of thepresent invention will become apparent to one with skill in the art uponexamination of the following drawings and detailed description. It isintended that all such aspects, systems, methods, features, advantages,and objects are to be included within this description, are to be withinthe scope of the present invention, and are to be protected by theaccompanying claims.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the invention and the advantagesthereof, reference is now made to the following description, inconjunction with the accompanying figures briefly described as follows.

FIG. 1 is a perspective view of a gradient lens in accordance withcertain exemplary embodiments.

FIG. 2 is a cross sectional view of the gradient lens of FIG. 1 inaccordance with certain exemplary embodiments.

FIG. 3 is a diagram showing the gradient lens of FIG. 1 focusingparallel rays of electromagnetic energy incident on a lens surface ofthe gradient lens from a direction substantially perpendicular to aplanar surface of the gradient lens in accordance with certain exemplaryembodiments.

FIG. 4 is a diagram showing the gradient lens of FIG. 1 focusingparallel rays of electromagnetic energy incident on a lens surface ofthe gradient lens from a direction substantially parallel to a planarsurface of the gradient lens in accordance with certain exemplaryembodiments.

FIG. 5 is a perspective view of a gradient lens in accordance withcertain exemplary embodiments.

FIG. 6 is a cross sectional view of the gradient lens of FIG. 5 inaccordance with certain exemplary embodiments.

FIG. 7 is a diagram showing the gradient lens of FIG. 5 focusingparallel rays of electromagnetic energy incident on a lens surface ofthe gradient lens from a direction substantially perpendicular to aplanar surface of the gradient lens in accordance with certain exemplaryembodiments.

FIG. 8 is a diagram showing the gradient lens of FIG. 5 focusingparallel rays of electromagnetic energy incident on a lens surface ofthe gradient lens from a direction substantially parallel to a planarsurface of the gradient lens in accordance with certain exemplaryembodiments.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

Certain exemplary embodiments provide a gradient lens capable offocusing electromagnetic rays received at a first lens surface onto asecond lens surface. The first lens surface and second lens surface caninclude convex surfaces protruding in opposite directions from asubstantially planar surface. The lens can include a gradient indexbetween the first surface and the planar surface and a gradient indexbetween the two convex surfaces. The lens can include two or moregradient layers, each gradient layer having an index of refractiondifferent than that of adjacent gradient layers. The gradient layers canfocus parallel rays of energy incident on the first surface onto a focalpoint at the second surface of the lens. As the parallel rays pass fromone gradient layer to the next, the rays are redirected toward the focalpoint. One or more waveguides can be disposed along the second surfaceto receive the rays of energy and to transmit rays of energy through thelens.

Exemplary gradient lenses will now be described more fully hereinafterwith reference to FIGS. 1-8, which illustrate representative embodimentsof the present invention. The invention can be embodied in manydifferent forms and should not be construed as limited to embodimentsset forth herein; rather, these embodiments are provided so that thisdisclosure will be through and complete, and will fully convey the scopeof the invention to those having ordinary skill in the art. Furthermore,all “example” or “exemplary embodiments” given herein are intended to benon-limiting, and among others supported by representations of thepresent invention.

Turning now to the drawings, in which like numerals indicate likeelements throughout the figures, exemplary embodiments are described indetail. FIGS. 1 and 2 illustrate a gradient lens 100 in accordance withcertain exemplary embodiments. In particular, FIG. 1 is a perspectiveview of a gradient lens 100 in accordance with certain exemplaryembodiments, and FIG. 2 is a cross sectional view of the gradient lens100 of FIG. 1 in accordance with certain exemplary embodiments.

Referring to FIGS. 1 and 2, the lens 100 includes a substantially planarsurface 105 and two convex lens surfaces 110 and 115. In this exemplaryembodiment, each lens surface 110 and 115 has a substantiallyhemispherical shape. In alternative exemplary embodiments, one or bothlens surfaces 110 and 115 may have a semispherical shape comprising aportion of a sphere less than or greater than that of a hemisphere. Incertain other exemplary embodiments, sides of the lens surface 110adjacent to the planar surface 105 may be flat rather than round. Incertain other exemplary embodiments, the lens surfaces 110 and 115 maybe non-spherical or zoned. In certain exemplary embodiments, one or bothlens surfaces 110 and 115 can be shaped to conform to the surface of anadjacent object, such as a radome, window, or aperture.

The lens surface 115 projects outward from the planar surface 105 whilethe lens surface 110 is opposite of and projects away from the planarsurface 105. The two lens surfaces 110 and 115 can be centrally alignedwith the planar surface 105. Although in this exemplary embodiment, thelens surface 115 is substantially smaller than lens surface 110, inalternative exemplary embodiments, the lens surfaces 110 and 115 mayhave more similar sizes or lens surface 115 may be larger than that oflens surface 110.

As depicted in FIG. 2, the lens 100 includes three gradient layers120-122 disposed between the two lens surfaces 110 and 115. The gradientlayers 120-122 are configured to redirect parallel rays ofelectromagnetic energy incident on the lens surface 110 toward a focalpoint on the lens surface 115. To accomplish this, the gradient layers120-122 generally provide a gradient index between the lens surface 110and 115. More particularly, the gradient layers 120-122 provide astep-wise increasing index of refraction from lens surface 110 to lenssurface 115. In this configuration, gradient layers 120-122 closer tothe surface 110 have a smaller index of refraction than gradient layers120-122 closer to lens surface 115. In certain exemplary embodiments,each gradient layer 120-122 has a uniform index of refraction that isdifferent than adjoining gradient layers 120-122.

In certain exemplary embodiments, the lens 100 may include a gradientimplemented as a continuum of dielectric change. Such an implementationmay be achieved through the use of conically tapered holes. These holescontrol an air-dielectric mix in the lens 100 material. Air has adielectric constant of approximately one, and is generally lower thanthe dielectric used in the lens 100. In these implementations, the largeradius end of the conical hole generates a lower dielectric constantthan the small radius end of the conical hole because the large radiusend introduces more air into the dielectric material, averaging down thenet dielectric constant. An example of a lens having a gradientimplemented as a continuum of dielectric change is described in U.S.Pat. No. 5,677,796, entitled “Luneberg Lens and Method of ConstructingSame,” filed on Aug. 25, 1995, the entire contents of which are herebyfully incorporated herein by reference.

As a ray passes from a medium having a lower index of refraction to amedium having a higher index of refraction at an angle that deviatesfrom perpendicular to the boundary between the two mediums, the ray isbent toward a normal perpendicular to the boundary. For example,considering that the index of refraction of air is approximately one, ifa ray propagating through air passes through the surface 110 into thegradient layer 120 having an index of refraction greater than one at anangle with respect to the point of the surface 110 that the ray passesthrough, the direction of the ray would be bent toward a normalperpendicular to a plane corresponding to that point on the surface 110.

The resultant direction of a ray that passes between mediums havingdiffering indices of refraction is dependant on the angle of incidenceof the ray with respect to the boundary's normal and the ratio of theindices of refraction of the two mediums. According to Snell's law, theangle of refraction (i.e., angle of ray in second medium with respect tothe normal) is given by Equation 1 below.

$\begin{matrix}{{\sin \; \theta_{2}} = {\frac{n_{1}}{n_{2}}\sin \; \theta_{1}}} & {{Equation}\mspace{14mu} 1}\end{matrix}$

In Equation 1, n₁ is the index of refraction of the medium from whichthe ray passes from and θ₁ is the angle of incidence of the ray withrespect to the boundary's normal. Likewise, n₂ is the index ofrefraction of the medium in which the ray passes to and θ₁ is the angleof refraction of the ray resulting from passing between the two mediums.As can be deciphered from Equation 1, the angle of refraction is smallerfor smaller ratios of n₁ to n₂. That is, a ray passing from a mediumhaving index of refraction n₁ to a medium having index of refraction ofn₂ will bend more toward the normal of the boundary with a larger n₂with respect to n₁.

As briefly described above, the gradient layers 120-122 of the lens areconfigured to redirect parallel rays of electromagnetic energy incidenton the lens surface 110 toward a focal point on the lens surface 115. Inthis exemplary embodiment, the lens 100 includes three gradient layers120-122, each gradient layer having a different index of refraction thaneach other gradient layer. In order to redirect rays incident on thesurface 110 toward a focal point on the lens surface 115, the index ofrefraction of gradient layer 120 is greater than that of gradient layer121 and the index of refraction of gradient layer 121 is greater thanthat of gradient layer 122. For example, the index of refraction ofgradient layer 120 may be 2.54, the index of refraction of gradientlayer 121 may be 4, and the index of refraction of gradient layer 122may be 9.

The gradient layer 122, which is bounded by lens surface 115, planarsurface 105, and gradient layer 121, comprises two solid hemisphericalregions 122A and 122B joined at their respective bases. Although in thisexemplary embodiment, region 122A is substantially larger than that ofregion 122B, in alternative exemplary embodiments, the regions 122A and122B can have substantially similar sizes. That is, the gradient layer122 can have a substantially spherical shape in alternative exemplaryembodiments. The gradient layers 120 and 121 are hemispherical shaped“shells” disposed concentrically between the gradient layer 122 and lenssurface 110. Although there are two hemispherical shell-like gradientlayers 120 and 121 in this exemplary embodiment, any number of shellsmay be used to provide a desired gradient index between the lens surface110 and the lens surface 115. Additionally, although not illustrated inFIG. 1, gradient layers in the form of hemispherical shells can also bedisposed over region 122B.

Each of the gradient layers 120-122 can comprise a solid dielectrichaving a substantially uniform index of refraction throughout thegradient layer 120-122. Some exemplary materials that can be used forthe gradient layers include TPX, REXOLITE, polytetrafluoroethylene(“TPFE”), polystyrene, and additives in a base material, such aspolystyrene. Each of the gradient layers 120-122 can comprisesubstantially similar materials having different indices of refractionor different materials. For example, the gradient layers 120 and 121 maycomprise REXOLITE, while the gradient layer 122 comprises polystyrene.Alternatively, or additionally, materials having a varying index ofrefraction can be used. For example, one or more of the gradient layers120-122 can comprise a Luneberg lens. Tapered holes in a material havinga large dielectric constant can achieve this effect as described in U.S.Pat. No. 5,677,796.

The lens 100 can be manufactured in various ways. For example, thegradient layer 122 can be manufactured by first constructing a sphericallens corresponding to a sphere having two hemispheres the size of region122A. Then, a portion of one hemisphere of the spherical lens can betrimmed to form the region 122B of the gradient layer 122. Next, ahemispherical shell can be glued or otherwise attached to the gradientlayer 122 over the region 121 to form the gradient layer 121. Finally, asecond hemispherical shell can be glued or otherwise attached overgradient layer 121 to form gradient layer 120. In another example, eachregion 122A and 122B of gradient layer 122 can be manufacturedseparately and glued together to form the gradient layer 122. In certainexemplary embodiments, components having the same or similar indices ofrefraction are integral as gluing two components may introduce airbetween two separate components.

The use of tapered holes as discussed earlier is another approach tomanufacturing the lens 100. The mixing in of air via the hole lowers thedielectric constant to the desired level. The slope of the hole controlsthe level through the depth of the hole to create the desired gradient.In this approach, the holes can be drilled or machined into a highdielectric material. The holes also can be part of an injection molddesign. The holes also can be fabricated using a sintered laserstereographic (“SLS”) technique.

FIGS. 3 and 4 are diagrammatical representations of the paths of twosets of parallel rays 160 and 165 of electromagnetic energy propagatingthrough the lens 100 of FIG. 1. FIG. 3 is a diagram showing the gradientlens 100 focusing parallel rays 160 of electromagnetic energy incidenton the lens surface 110 of the gradient lens 100 from a directionsubstantially perpendicular to the planar surface 105 of the gradientlens 100 in accordance with certain exemplary embodiments. FIG. 4 is adiagram showing the gradient lens 100 focusing parallel rays 165 ofelectromagnetic energy incident on the lens surface 110 of the gradientlens 100 from a direction substantially parallel to the planar surface105 of the gradient lens 100 in accordance with certain exemplaryembodiments. These diagrams illustrate how parallel rays incident fromdifferent directions can be focused onto different focal points on thesurface 115 of the gradient lens 100.

Referring to FIG. 3, a plurality of parallel electromagnetic rays 160are incident on the surface 110 of the gradient lens 100 in a directionsubstantially perpendicular to the planar surface 105. For the purposesof this explanation, the ambient medium may have an index of refractionof one and the indices of refraction of the gradient layers 120-122 havestep-wise increasing indices of refraction from the gradient layer 120to the gradient layer 122, each gradient layer 120-122 having an indexof refraction greater than one. That is, the index of refraction ofgradient layer 122 is greater than that of gradient layer 121, the indexof refraction of gradient layer 121 is greater than that of gradientlayer 120, and the index of refraction of gradient layer 120 is greaterthan that of the medium from which the rays 160 are propagating from.

As the rays 160 pass through the surface 110 into the gradient layer120, each of the rays that deviates from perpendicular to the surface110 where the ray passes through bends inward toward a normalperpendicular to a plane corresponding to the surface 110 where the raypasses through. Outermost rays with respect to the center of the planarsurface 105 tend to bend more as the angle of incidence of the outermostrays is greater than the angle of incidence of the innermost rays.

Because the gradient layer 120 comprises a substantially uniform indexof refraction, after the rays 160 bend passing through the lens surface110, the rays 160 can continue on a substantially straight path untilreaching a boundary between gradient layers 120 and 121. As the index ofrefraction of gradient layer 121 is greater than that of gradient layer120, the rays 160 that deviate from perpendicular to the boundary wherethe ray passes is bent toward a normal perpendicular to a planecorresponding to the boundary where the ray passes through. Likewise, asthe rays 160 pass from gradient layer 121 to gradient layer 122, therays 160 are further bent toward a normal corresponding to a boundarybetween the gradient layers 121 and 122. The rays 160 then continuealong this path until reaching a focal point 130 on the lens surface115.

Referring now to FIG. 4, a plurality of parallel electromagnetic rays165 are incident on the surface 110 of the gradient lens 100 in adirection substantially parallel to the planar surface 105. Similar tothe rays 160, the rays 165 that deviate from perpendicular to thesurface 110 where the ray passes through bends inward toward a normalperpendicular to a plane corresponding to the surface 110 where the raypasses through. As the rays 165 pass through each boundary between thegradient layers 120-122, the rays 165 are further bent toward a focalpoint 135 on the surface 115 of the lens 100.

The lens 100 can be used in many different applications, including thosethat would benefit from parallel rays being focused onto a focal pointof a lens surface. For example, the lens 100 is particularly useful inantenna communications. Referring to FIGS. 3 and 4, antenna feedelements 140 and 145 can be disposed on the lens surface 115 to receivethe rays 160 and 165, respectively. In particular, antenna feed element140 is disposed on the lens surface 115 at the focal point 130 toreceive the rays 160. Similarly, antenna feed element 145 is disposed onthe lens surface 115 at the focal point 135 for receiving the rays 165.The location of the antenna feed element 145 to receive the rays 165 maybe determined based upon the gradient design for the lens 100. In orderto receive (and transmit) rays in substantially all directions via thelens 110, antenna feed elements can be disposed in three dimensionsaround the convex shaped lens surface 115. Additionally, the lens 100can be used in an antenna system such as the multi-beam antenna systemdescribed in U.S. patent application Ser. No. 12/322,592, entitled“Modal Beam Positioning,” filed on Feb. 4, 2009, the entire contents ofwhich are hereby fully incorporated herein by reference. In such anembodiment, a network of antenna feed elements can be disposed aroundthe lens surface 115.

FIGS. 5 and 6 illustrate a gradient lens 500 in accordance with certainexemplary embodiments. FIG. 5 is a perspective view of a gradient lens500 in accordance with certain exemplary embodiments. FIG. 6 is a crosssectional view of the gradient lens 500 of FIG. 5 in accordance withcertain exemplary embodiments. The gradient lens 500 is an alternativeembodiment to that of gradient lens 100 of FIGS. 1-4. The gradient lens500 includes features to support a low profile installation that canconform to the shape of a radome, window, or aperture in which thegradient lens 500 is installed. In certain exemplary embodiments, theouter layers of the gradient may be designed to function as a radome.

Referring to FIGS. 5 and 6, the gradient lens 500 includes asubstantially planar surface 505 and two convex lens surfaces 510 and515. In this exemplary embodiment, the lens surface 515 has asubstantially hemispherical shape while the lens surface 510 has asemispherical shape comprising a portion of a sphere less than that of ahemisphere. The lens surface 515 projects outward from the planarsurface 505 while the lens surface 510 is opposite of the planar surface505 and projects away from the planar surface 505. The two lens surfaces510 and 515 can be centrally aligned with the planar surface 505. Incertain exemplary embodiments, the lens surfaces 510 and 515 may benon-spherical shaped or zoned. In certain exemplary embodiments, one orboth lens surfaces 510 and 515 can be shaped to conform to the surfaceof an adjacent object, such as a radome or window, or to an aperture.

As depicted in FIG. 6, the lens 500 includes eight gradient layers520-527 disposed between the lens surface 510 and the planar surface505. Similar to the gradient lens 100 of FIG. 1, the gradient lens 500is configured to redirect parallel rays of electromagnetic energyincident on the lens surface 510 toward a focal point on the lenssurface 515. The gradient layers 520-527 likewise provide a gradientindex between the lens surfaces 510 and 515 in the form of a step-wiseincreasing index of refraction from lens surface 510 to lens surface515. That is, the index of refraction of gradient layers 520-526disposed further from gradient layer 527 have smaller indices ofrefraction that gradient layers 520-526 disposed closer to gradientlayer 527. Each of the gradient layers 520-527 can comprise a soliddielectric having a substantially uniform index of refraction throughoutthe gradient layer 520-527. Alternatively, or additionally, materialhaving a varying index of refraction can be used in the gradient layers520-527 of the gradient lens 500. The same or similar dielectricmaterials as those used to form the gradient layers 120-122 of gradientlens 100 also can be used to form the gradient layers 520-527 ofgradient lens 500. In certain exemplary embodiments, the lens 500 mayinclude a gradient implemented as a continuum of dielectric change asdescribed above with reference to FIG. 2. In certain exemplaryembodiments, sides of the lens surface 510 adjacent to the planarsurface 505 may be flat rather than round.

The gradient lens 500 differs from that of the gradient lens 100 ofFIGS. 1-4 in the shape and configuration of the gradient layers. In thegradient lens 100, each of the gradient layers 120 and 121 that werearranged as shells around the gradient layer 122 have a substantiallyhemispherical shape. The gradient lens 500 includes a substantiallyspherical gradient layer 527 and semispherical gradient layers 520-526arranged as shells around the substantially spherical gradient layer527. Instead of each shell-like gradient layer 520-526 having ahemispherical shape, only the gradient layer 526 disposed directly overthe substantially spherical gradient layer 527 has a hemisphericalshape. Each other shell-like gradient layer 520-525 comprises only aportion of a hemispherical shape. These shapes can be limited by thelens surface 510. Although in this exemplary embodiment, the lens 500includes one hemispherical shaped gradient layer 526 and multiplesemispherical gradient layers 520-525, the lens 500 can include anynumber of hemispherical gradient layers and any number of semisphericalgradient layers.

The lens 500 can support a lower profile design than that of lens 100.That is the lens 500 can have a smaller height (measured from a peak onlens surface 510 to a peak on lens surface 515) to width (diameter ofplanar surface 505) ratio than that of lens 100. To support this lowerprofile design, the gradient layers 520-527 can have a more rapidlyincreasing gradient index from lens surface 510 to lens surface 515.Thus, the gradient layers 520-527 may bend rays of electromagneticenergy incident on the lens surface 510 more rapidly toward a focalpoint at the lens surface 515.

The lens 500 can be manufactured in various ways. For example,hemispherical shaped gradient layer 526 can be glued or otherwiseattached to one half of substantially spherical shaped gradient layer527. A hemispherical shell corresponding to each other gradient layer520-525 can be attached, one at a time, over the gradient layer 527.After all of the gradient layers 520-527 are attached, the upper portionof the lens 510 can be trimmed to form the lens surface 510.Alternatively, each gradient layer 520-527 can be manufacturedindependently into its final form and attached to create the lens 510.Additionally, the lens 500 may be manufactured with tapered holes asdescribed above with reference to FIG. 2.

FIGS. 7 and 8 are diagrammatical representations of the paths of twosets of parallel rays 560 and 565 of electromagnetic energy propagatingthrough the lens 500 of FIG. 5. FIG. 7 is a diagram showing the gradientlens 500 focusing parallel rays 560 of electromagnetic energy incidenton the lens surface 510 of the gradient lens 500 from a directionsubstantially perpendicular to the planar surface 505 of the gradientlens 500 in accordance with certain exemplary embodiments. FIG. 8 is adiagram showing the gradient lens 500 focusing parallel rays 565 ofelectromagnetic energy incident on the lens surface 510 of the gradientlens 500 from a direction substantially parallel to the planar surface505 of the gradient lens 500 in accordance with certain exemplaryembodiments. These diagrams illustrate how parallel rays incident fromdifferent directions can be focused onto different focal points on thesurface of the lens 510.

Referring to FIG. 7, a plurality of parallel electromagnetic rays 560are incident on the surface 510 of the gradient lens 500 in a directionsubstantially perpendicular to the planar surface 505. For the purposesof this explanation, the ambient medium may have an index of refractionof one and the indices of refraction of the gradient layers 520-527 havestep-wise increasing indices of refraction from the gradient layer 520to gradient layer 527, each gradient layer 520-527 having an index ofrefraction greater than one.

As the rays 560 pass through the surface 510 into the gradient layer520, each of the rays that deviates from perpendicular to the surface510 where the ray passes through bends inward toward a normalperpendicular to a plane corresponding to the surface 510 where the raypasses through. Outermost rays with respect to the center of the planarsurface 505 tend to bend more as the angle of incidence of the outermostrays is greater than the angle of incidence of the innermost rays. Asthe rays 560 pass through each boundary between adjacent gradient layers520-527, the rays 560 are further bent toward a focal point 570 on thesurface 515 of the lens 500.

Referring now to FIG. 8, a plurality of parallel electromagnetic rays565 are incident on the surface 510 of the gradient lens 500 in adirection substantially parallel to the planar surface 505. Similar tothe rays 560, the rays 565 that deviate from perpendicular to thesurface 510 where the ray passes through bends inward toward a normalperpendicular to a plane corresponding to the surface 510 where the raypasses through. As the rays 565 pass through each boundary betweenadjacent gradient layers 520-527, the rays 565 are further bent toward afocal point 575 on the surface 515 of the lens 500.

The lens 500 also can be used in antenna applications similar to that oflens 100. Referring to FIGS. 7 and 8, antenna feed elements 540 and 545can be disposed on the lens surface 515 to receive the rays 560 and 565,respectively. In particular, antenna feed element 540 is disposed on thelens surface 515 at the focal point 570 to receive the rays 560.Similarly, antenna feed element 545 is disposed on the lens surface 515at the focal point 575 for receiving the rays 565. In order to receive(and transmit) rays in substantially all directions via the lens 510,antenna feed elements can be disposed in three dimensions around theconvex shaped lens surface 515. The location of the feed 545 to receivethe rays 565 can be determined based upon the gradient design of thelens 500.

One of ordinary skill in the art would appreciate that the presentinvention supports a gradient lens capable of focusing electromagneticrays received at a first lens surface onto a second lens surface. Thefirst lens surface and second lens surface can include convex surfacesprotruding in opposite directions from a substantially planar surface.The lens can include a gradient index between the first surface and theplanar surface and a gradient index between the two convex surfaces. Thelens can include two or more gradient layers, each gradient layer havingan index of refraction different than that of adjacent gradient layers.The gradient layers can focus parallel electromagnetic rays incident onthe first surface onto a focal point at the second surface of the lens.As the parallel electromagnetic rays pass from one gradient layer to thenext, the rays are redirected toward the focal point.

Although specific embodiments have been described above in detail, thedescription is merely for purposes of illustration. It should beappreciated, therefore, that many aspects of the invention weredescribed above by way of example only and are not intended as requiredor essential elements of the invention unless explicitly statedotherwise. Various modifications of, and equivalent steps correspondingto, the disclosed aspects of the exemplary embodiments, in addition tothose described above, can be made by a person of ordinary skill in theart, having the benefit of this disclosure, without departing from thespirit and scope of the invention defined in the following claims, thescope of which is to be accorded the broadest interpretation so as toencompass such modifications and equivalent structures.

1-23. (canceled)
 24. A method for receiving parallel rays at a gradientlens, comprising the steps of: receiving a first plurality ofsubstantially parallel rays incoming from a first direction at a firstsurface of the lens; receiving a second plurality of substantiallyparallel rays incoming from a second direction at the first surface ofthe lens, the second direction being substantially different than thefirst direction; focusing the first plurality of substantially parallelrays onto a first focal point on a second surface of the lens; andfocusing the second plurality of substantially parallel rays onto asecond focal point on the second surface of the lens, the second focalpoint being different than the first focal point.
 25. The method ofclaim 24, wherein the first and second surfaces of the lens comprise aconvex shape.
 26. The method of claim 24, wherein the lens comprises agradient index between the first surface of the lens and the secondsurface of the lens.
 27. The method of claim 26, wherein the lenscomprises a plurality of gradient layers disposed inside the lensbetween the first and second surfaces of the lens.
 28. The method ofclaim 27, wherein adjacent gradient layers comprise different indices ofrefraction.
 29. The method of claim 28, wherein gradient layers closerto the first surface of the lens comprises an index of refraction lessthan that of gradient layers closer to the second surface of the lens.30. The method of claim 27, wherein the step of focusing the firstplurality of substantially parallel rays onto the first focal pointcomprises the step of bending at least a portion of the first pluralityof substantially parallel rays toward the first focal point as the firstplurality of substantially parallel rays pass from one gradient layer toan adjacent gradient layer.